What is the extreme y=9-6x^2,-2<= x<= 3 ?

The extreme y=9-6x^2,-2<= x<= 3 is Minimum(-2,-15),Maximum(0,9),Minimum(3,-45)

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extreme y=9-6x^2,-2<= x<= 3

extreme points

y = 9 - 6 x^{2}, - 2 \leq x \leq 3

Minimum (- 2, - 15), Maximum (0, 9), Minimum (3, - 45)

Solution steps

Find the critical points:

x = - 2, x = 0, x = 3

Domain of

9 - 6 x^{2}, - 2 \leq x \leq 3 : - 2 \leq x \leq 3

Find intervals:

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 3

Plug the extreme point

x = - 2

into

9 - 6 x^{2} \Rightarrow y = - 15

Minimum (- 2, - 15)

Plug the extreme point

x = 0

into

9 - 6 x^{2} \Rightarrow y = 9

Maximum (0, 9)

Plug the extreme point

x = 3

into

9 - 6 x^{2} \Rightarrow y = - 45

Minimum (3, - 45)

Minimum (- 2, - 15), Maximum (0, 9), Minimum (3, - 45)

f (x) = 2 x^{3} + 4 x^{2} - 1

49 x + \frac{1}{x}

f (x) = - 0.1 x^{2} + 1.2 x + 5

7 (x - 8)^{3}

y = \frac{x ^{2} - 5}{x - 3}

What is the extreme y=9-6x^2,-2<= x<= 3 ?
The extreme y=9-6x^2,-2<= x<= 3 is Minimum(-2,-15),Maximum(0,9),Minimum(3,-45)